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Lévy processes, i.e. processes in continuous time with stationary and independent increments, are named after Paul Lévy, who made the connection with infinitely divisible distributions and described their structure. They form a flexible class of models, which have been applied to the study of storage processes, insurance risk, queues, turbulence, laser cooling, ... and of course finance, where the feature that they include examples having "heavy tails" is particularly important. Their sample path behaviour poses a variety of difficult and fascinating problems. Such problems, and also some related distributional problems, are addressed in detail in these notes that reflect the content of the course given by R. Doney in St. Flour in 2005.

Lévy processes. --- Lévy, Processus de --- Electronic books. -- local. --- Lévy processes. --- Random walks (Mathematics). --- Lâevy processes --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Mathematical Statistics --- Random walks (Mathematics) --- Lévy, Processus de --- EPUB-LIV-FT SPRINGER-B --- Additive process (Probability theory) --- Random walk process (Mathematics) --- Walks, Random (Mathematics) --- Mathematics. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Math --- Science --- Stochastic processes --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities